Fumigation of particulate commodities

ABSTRACT

When fumigating a bulk particulate commodity stored in a top-vented vertical silo by slowly passing a gas containing a low concentration of a gaseous fumigant through the bulk mass, differences between the temperature, T g , in the bulk mass and the ambient temperature, T a , outside the silo cause a &#34;chimney effect&#34; within the silo, and possible unwanted dilution of the fumigant. The chimney effect also occurs in other top-vented storage structures containing particulate commodities. To overcome the chimney effect, the fumigant-containing gas is supplied through a duct to the base of the storage structure at a flow rate Q f  (in m 3  sec 1 ) determined by the relationship ##EQU1## where g is the acceleration due to gravity (approximately 9.8 m sec  2 ); P a  is the atmospheric pressure expressed in Pascals; R a  is the gas constant for air (=287 J kg -1  K -1 ); T a  is in K; T g  is also in K; R is a resistance factor (in Pascals sec m -2 ) which depends upon the nature of the commodity in the storage structure; and A is the horizontal cross-sectional area of the storage structure, in square meters. This technique can also be used to maintain effective fumigation of a plurality of storage structures in a storage facility, from a single source of gaseous fumigant.

TECHNICAL FIELD

This invention concerns the fumigation of stored particulate commoditiesthat are susceptible to attack and spoilage by insect pests. It isparticularly useful in the controlled fumigation of particulatefoodstuff (for example, grain) that is stored in a vertical silo whichis vented at the top. However, this invention is not limited in itsapplication to foodstuffs, or to commodities stored in silos.

BACKGROUND OF THE INVENTION

A technique for the effective and efficient fumigation of grain, usinglow concentrations of phosphine as the fumigant gas, is described in thespecification of International patent application No PCT/AU90/00268,which is WIPO Publication No 91/00017. That technique requires theestablishment of a slight over-pressure of the fumigant-containing gasin the grain, to the extent that the fumigant-containing gas flowsthrough the grain mass at a constant linear velocity and leaves the topsurface of the grain in the silo at a velocity in the range of from0.5×10⁻⁴ to 2×10⁻⁴ meters per second. The concentration of phosphine inthe gas passing through the grain is in the range of from 4 to 200micrograms per liter.

While that technique works well, further work in connection with itscommercial adoption has shown that a problem arises when grain in avertical silo is being fumigated and the temperature within the silo isdifferent from the ambient air temperature outside the silo. When thetemperature of the grain is greater than the outside ambient airtemperature, the density of the air within the silo is less than thedensity of the air outside, and there is a tendency for the air insidethe silo to rise. This phenomenon has been termed the "chimney effect".The difference in density between the air inside the silo and the airoutside the silo produces a difference between the pressure gradientwith height inside the silo and the pressure gradient with heightoutside the silo. Hence, in a top vented silo, the air pressure in thegrain at the base of the silo will be different from the air pressureoutside the silo at the level of the base of the silo.

In this situation, if the bottom of the silo is not completely sealed(in commercial silos, this is usually the case, for even notionallysealed bases contain cracks and crevices which permit the ingress ofair), the chimney effect causes an airflow through a top vented silo.This flow of air through the silo will dilute the concentration offumigant within at least part of the grain mass or other foodstuffstored in the silo, and may prevent effective fumigation of the storedproduct.

The same chimney effect occurs in other forms of storage structureswhich are vented at their tops and not completely sealed at their bases.Thus, for convenience, in the remainder of this specification (includingthe claims), the term "silo" will include within its scope any form ofstorage structure in which a particulate commodity may be stored.

DISCLOSURE OF THE PRESENT INVENTION

The prime object of the present invention is to provide a techniquewhich compensates for the chimney effect, and prevents an undesirabledilution of fumigant during the fumigation of the charge of a top ventedsilo.

This objective is achieved by maintaining (and preferably continuouslyadjusting) the flow rate of the fumigant-containing gas so that, evenwhen the chimney effect is present, there is sufficient fumigant gaspresent to ensure continuous fumigation of the stored product. It hasbeen found that the required adjustment of the flow rate depends uponthe difference between the temperature of the stored product and theambient temperature outside the silo. Thus the necessary modification ofthe flow rate of the fumigant-containing gas to compensate for thechimney effect, by maintaining a small positive pressure of apredetermined concentration of fumigant within the grain mass or otherstored product, can be determined from measurements or estimates of thetemperatures within and outside the silo.

According to the present invention, a method of effective fumigation ofa particulate commodity stored in a silo comprises the steps of

(a) providing a supply of a fumigant-containing gas having a fumigantconcentration which is effective to control insect pests in the storedcommodity when applied to the stored commodity for an extended period;and

(b) supplying the fumigant-containing gas to the base of the silo at arate, Q_(f), which, if the silo is full, is determined by therelationship ##EQU2## where Q_(f) is expressed in m³ sec⁻¹ ; g is theacceleration due to gravity (approximately 9.8 m sec ⁻²); P_(a) is theatmospheric pressure expressed in Pascals; R_(a) is the gas constant forair (=287 J kg⁻¹ K⁻¹); T_(a) is the temperature of the air outside thesilo, expressed in K; T_(g) is the temperature of the commodity withinthe silo, also in K; R is a resistance factor (in Pascals sec m⁻²) whichdepends upon the nature of the stored commodity in the silo; and A isthe horizontal cross-sectional area of the silo, in m².

Also according to the present invention, apparatus for fumigating aparticulate commodity stored in a silo comprises

(a) means for pumping a fumigant-containing gas into the base of thesilo;

(b) a first temperature sensing device positioned within the commodityin the silo and having a first output signal indicative of thetemperature within the stored commodity;

(c) a second temperature sensing device positioned outside the silo andhaving a second output signal indicative of the ambient temperatureoutside the silo;

(d) processing means adapted to receive said first and second outputsignals and generate at least one control signal; said at least onecontrol signal being input to control means; said control means beingadapted to control the rate at which said gas pumping means pumps thefumigant-containing gas so that the rate of flow of thefumigant-containing gas into the silo has a value, Q_(f), which, if thesilo is full, is determined by the relationship ##EQU3## where Q_(f) isexpressed in m³ sec⁻¹ ; g is the acceleration due to gravity(approximately 9.8 m sec⁻²); P_(a) is the atmospheric pressure expressedin Pascals; R_(a) is the gas constant for air (=287 J kg⁻¹ K⁻¹); T_(a)is the temperature of the air outside the silo, expressed in K; T_(g) isthe temperature of the commodity stored within the silo, also in K; R isa resistance factor (in Pascals sec m⁻²) which depends upon the natureof the commodity stored in the silo; and A is the horizontalcross-sectional area of the silo, in m².

The resistance factor R, as noted above, is dependent on the nature ofthe commodity stored in the silo and the way in which it has beenstored. For loosely packed wheat, the constant R is about 3100, whilefor closely packed wheat, it has a value of approximately 4000. Theresistance factor, R, is well-known to agricultural engineers, havingbeen determined experimentally for a number of different cereal grainsand other commodities. In fact, one of the present inventors (Dr A JHunter) has tabulated values for the factor R for a number of seedcommodities in Table 2 of his paper entitled "Pressure Difference acrossan Aerated Seed Bulk for some Common Duct and Storage Cross-sections",which was published in the Journal of Agricultural Engineering Research,Volume 28, pages 437 to 450, 1983. The contents of that paper areincorporated into this specification by this reference to that paper.Relevant data from said Table 2, for commodities other than wheat, arereproduced (also in tabular form) below

    ______________________________________                                                           Moisture                                                   Commodity          Content   R (in Pa s m.sup.-2)                             ______________________________________                                        Alfalfa            7%        16,318                                           Barley             12%       1,676                                            Clover, alsike     dry       27,263                                           Clover, crimson    8%        10,455                                           Clover, red        dry       17,626                                           *Corn, clean ear   16%       6.19                                             **Corn, ear, as harvested                                                                        20%       128                                              Corn, shelled      12.4%     719                                              Fescue             11%       4,722                                            Flax               11%       10,421                                           Grass seed, brome  10.5%     1,535                                            Grass seed, rescue 13%       709                                              Kobe Lespedeza     15.5%     3,167                                            Lupin seed, blue   7.5%      512                                              Oats               13%       1,816                                            *Pea beans         15%       435                                              *Peanuts in shell  4.4%      29.0                                             Popcorn, shelled, yellow pearl                                                                   12%       1,046                                            type                                                                          Popcorn, white rice type                                                                         14%       1,766                                            Rice, rough        13%       1,952                                            Sericea Lespedeza  13%       16,318                                           Sorghum, grain     13%       2,664                                            Soybeans           10%       646                                              Wheat              11%       3,131                                            Linseed, glenelg   7.9%      14,907                                           Rapeseed, tower    5.7%      7,097                                            Safflower, gila    5.9%      1,207                                            Sunflower, commercial crushing                                                                   7.9%      1,593                                            ______________________________________                                         *Approximate value only as insufficient data were available to enable         accurate values of R to be established directly in these cases.          

The currently preferred fumigant for use with stored cereal grains andother particulate foodstuff is phosphine, although the present inventionmay be used with methyl bromide, carbonyl sulphide or any other suitablegaseous fumigant.

For a better understanding of the present invention, a more detaileddescription of the controlled fumigation method and examples of itspractical implementation will now be provided.

DETAILED DESCRIPTION OF THE FUMIGATION METHOD

As the present invention has a major application to the fumigation ofstored grain, the following description will concentrate on thisapplication of the invention, although it is emphasised that the presentinvention may be used for the fumigation of any other particulatecommodity that is stored in a vertical silo or in any other storagestructure in which the chimney effect may occur.

Grain stored in a silo is essentially a porous mass. There arecontinuous air paths from the top of the grain mass to the bottom of thegrain mass. If the silo is a top vented (or open topped) vertical silo,the bottom or base of which is completely sealed, the difference betweenthe pressure at the bottom of the grain mass within the silo and theoutside atmospheric pressure at the same level, known as thedifferential static pressure, .increment.P₁, is given by therelationship. ##EQU4## where .increment.P₁ is in Pascals; g is theacceleration due to gravity (9.8 m sec ⁻²); h is the height of the grainmass in meters; P_(a) is the atmospheric pressure (in Pascals); R_(a) isthe gas constant for air (=287 J kg⁻¹ K⁻¹); T_(a) is the ambienttemperature outside (and thus adjacent to the top of) the silo, in K;and T_(g) is the temperature of the grain, also in K.

If the bottom of the silo is completely leaky and air flows freely intothe base of the silo, the differential static pressure (inside tooutside) would be zero. If the bottom of the silo is partially sealed,the measured differential static pressure, .increment.P₂, at the base ofthe grain mass will be a value between zero and .increment.P₁. The ratio.increment.P₂ /.increment.P₁ is therefore a measure of how well thebottom of the silo has been sealed.

If the grain temperature is greater than the temperature outside thesilo and the bottom of the silo is not completely sealed, the chimneyeffect will cause air from outside the silo to flow into the base of thesilo, to dilute the concentration of fumigant inside the silo. Thisingress of air will cause the fumigation of the stored grain to fail,either totally or in part.

More generally, if the sealing of the silo at the top or the bottom isnot specified, .increment.P may be taken as the pressure differencebetween the inside and the outside of the sili, and .increment.P₂ isgiven by:

    .increment.P.sub.2 =|.increment.P.sub.T -.increment.P.sub.B |

where the pressure differences .increment.P_(T) and .increment.P_(B) aredefined as pressure differentials, with reference to pressures insidethe silo and outside the silo at the same level; .increment.P_(T) ismeasured at the top of the silo; and .increment.P_(B) is measured at thebottom or base of the silo.

Thus the flow of air within a full silo, due to the chimney effect, isgiven by Q_(c), where ##EQU5## where A is the cross-sectional area ofthe silo, in m² ; R is the grain resistance factor (which, as notedabove, is about 3100 for loose wheat and about 4000 for packed wheat); his the height of the silo in meters; and Q_(c) is in m³ sec⁻¹.

As the difference between the ambient temperature and the graintemperature changes, the flow due to the chimney effect will change andthe pressure differentials will also change. Thus the flow of thefumigant-containing gas which is necessary to overcome the flow due tothe chimney effect and just maintain the required small positivepressure within the grain mass will also change. The modified flow rate,as has been shown, may be determined from measurements of thetemperature of the grain and the ambient temperature. To overcome thechimney effect flow, Q_(c), a fumigant gas flow into the base of thesilo at a rate of Q_(f) is needed. This input flow will produce anescape (or grain face) velocity, v_(f), expressed in m sec⁻¹, of:##EQU6## where R_(a) is the gas constant for air, which is 287 J kg⁻¹K⁻¹.

Hence the required flow, Q_(f), of fumigant-containing gas for a fullsilo is given by: ##EQU7##

As noted above, when operating a fumigation system for stored grain, thebase of the silo is rarely completely sealed. Thus the formulae derivedabove will be applicable to almost all top vented silos and the flowrate of a fumigant-containing gas that is required to maintain theefficacy of the fumigation of the silo charge can be ascertained by thefollowing steps:

(1) determine the average temperature of the grain, T_(g), in K;

(2) determine the ambient temperature outside the silo, T_(a), in K;

(3) determine the cross-sectional area of the silo in m² ; then

(4) determine, using the above formula, the required flow rate Q_(f).

If the grain is not cooled artificially and the fumigation system isrequired to run unattended, with a pre-determined steady flow offumigant-containing gas that is maintained at all times, it will benecessary to obtain an estimate of the minimum outside (ambient)temperature, T_(a), for the period of unattended fumigation. The maximumchimney effect will occur at this minimum value of T_(a). The maximumvalue of the flow rate, Q_(f), of the fumigant-containing gas, whichwill occur at this value of T_(a), will then be calculated. If thismaximum value of Q_(f) is adopted for the fumigation system, at no timeduring the unattended fumigation will the concentration of fumigant fallbelow the required concentration that has been established fromtoxicology data.

In some grain storage facilities, the difference between the graintemperature, T_(g), and the outside air temperature, T_(a), may bepositive or negative (for example, in geographical areas wheras theambient temperature can be expected to exceed the temperature of grainstored in a vertical silo in the area, and in those instances wherethere is artificial cooling of grain stored in a vertical silo). WhenT_(a) exceeds T_(g), a negative chimney effect will occur in a silo thatis not fully sealed at its top and bottom. With a negative chimneyeffect, the air flow through the silo will be downwards. In thissituation, to achieve efficient unattended fumigation of the grain mass,a positive value of the flow rate Q_(f) of the fumigant-containing gas,which will compensate for the maximum absolute value of the expectedpositive and/or negative chimney effects in the silo, is required andshould be maintained at all times.

When minimum consumption of the fumigant is required while maintainingeffective fumigation, the outside ambient temperature and thetemperature of the grain mass should be monitored continuously and theflow rate adjusted, as necessary, to obtain the value of Q_(f)calculated from the observed temperatures T_(a) and T_(g).

It should also be noted that when a variable (controlled) flow rateQ_(f) is established for the fumigation of a particulate charge of avertical silo, and the temperature of the silo charge (the grain mass)fluctuates between a value greater than the ambient temperature outsidethe silo and a temperature which is lower than the outside ambienttemperature, a positive value of Q_(f) should be established at alltimes.

In principle, a net flow rate through the grain mass of zero would notbe detrimental to the fumigation of the grain. The requiredconcentration of fumigant that is determined by toxicologicalconsiderations would be established in the grain mass before the flow offumigant-containing gas ceases, and--ignoring the adsorption of fumigantby the grain, which is very low--would not be reduced.

Continuous control of the flow rate of fumigant-containing gas into atop vented silo can be effected manually (for example, by monitoring thedifference between the temperature of the grain in a silo and theambient air temperature outside the silo, then selecting--from a numberof pre-set controlled flow rate values--the pre-determined flow ratevalue for the observed temperature difference). Such a manual controlsystem, however, will rarely be the most cost-effective form ofcontinuous control. Continuous control is preferably effected using acontrol mechanism which is responsive to signals generated bytemperature sensors positioned within the grain and outside the silo. Ifdesired, an average value of the grain temperature may be determined bypositioning a number of sensors at different respective locations withinthe grain mass, and generating (by known means) an input signal for thecontrol mechanism which is proportional to the difference between theaverage of the output signals of the temperature sensors in the grainand the ambient air temperature outside the silo. The control unit willnormally be a programmed microprocessor or programmed mini-computerwhich generates an output signal which, in turn, is used to adjust aflow control device, so that the actual flow rate of thefumigant-containing gas is substantially the calculated value of Q_(f).

It will be appreciated that if the fumigant is added to its carrier gas(usually air) after the required flow rate has been determined, theinput of fumigant into the carrier gas has to be varied in parallel withthe variations in the flow rate of the carrier gas, to maintain thepredetermined concentration of fumigant within the silo, which is basedupon toxicological considerations.

A practical full-scale implementation of the present invention will nowbe described, by way of example only, with reference to the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of phosphine supply and control equipmentinstalled for use with a top-vented vertical grain silo.

FIG. 2 is a representation, in graph form, of data obtained in oneexample of the use of the arrangement shown in FIG. 1.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENT

Full-scale testing of the present invention has been carried out atWallendbeen, New South Wales, Australia, with a top-ventilated verticalgrain silo holding 2,000 tonnes of wheat. The phosphine delivery andcontrol equipment used for this full scale testing is shown in

FIG. 1. The tests with this equipment began in February 1994 and arecontinuing to August 1994 (and possibly beyond that date).

In the arrangement shown in FIG. 1, three temperature sensors 12 (anyrequired number of temperature sensors could be used) are installed tomeasure the temperature at different locations within the bulk grain 11stored in the vertical silo 10, and a single temperature sensor 12Amonitors the ambient temperature outside the grain silo. The outputsignals from the temperature sensors are input to a programmedmicroprocessor 13 (a 386 PC made by Australian Computer Technology PtyLtd is included in the apparatus installed at Wallendbeen, but any othersuitable microprocessor could be used). The microprocessor 13 averagesthe temperature signals from the sensors 12 and determines thedifference between that average signal value and the signal from thetemperature sensor 12A. From this difference value, the microprocessor13 calculates a value of the required flow rate, Q_(f), of thefumigant-containing gas. When the fumigation is initiated, apredetermining value of Q_(f) is established.

The microprocessor 13 also receives signals from a flow sensor 23 (forexample, an ALNOR thermo-anemometer, Model No GGA-26) which is mountedin a duct 18 leading to the base of the silo 10. The microprocessorcompares the actual flow rate with its calculated value of Q_(f). If theactual flow in the duct 18 is greater than the calculated value ofQ_(f), a signal is sent to the controller 14, to cause it to close avalve 21 to reduce the flow of air in the duct 18, which is establishedby an industrial blower 15. The end of the duct 18 which is remote fromthe blower 15 is adjacent to a distributor plate (which need not be ahorizontal distributor plate 25, as shown in FIG. 2) at the base of thesilo 10. If the actual flow of air through the duct 18 is less than thecalculated value of Q_(f), a signal to the controller 14 causes thecontroller to open the valve 21.

The opening (or closing) of the valve 21 is effected in increments, andis continued until the flow rate in the duct 18 is equal to thecalculated value of Q_(f), whereupon the microprocessor signal to thecontroller 14 is changed to a value which causes the controller 14 toneither open nor close the valve 21.

The microprocessor 13 also receives a signal from a fumigantconcentration sensor 22 (for example, a CO cell manufactured by CityTechnology in the United Kingdom) which measures the concentration offumigant in the air flowing through the duct 18. The sensor 22 is not inthe duct 18, but receives a sample of the fumigant-containing gasflowing through the duct and obtains the fumigant concentration value ofthe sample by comparison with a calibrant mixture from a cylinder 26. Ifthe fumigant concentration signal from the sensor 22 shows that thefumigant concentration is below (or above) the required value (therequired value is stored in the memory of the microprocessor), themicroprocessor 13 sends a signal to the controller 16, to cause it toopen (or close) the valve 17, which controls the supply of phosphinefrom a cylinder 20 (or other source of fumigant--for example, an on-sitegenerator) to the airflow in the duct 18. The opening (or closing) ofthe valve 17 is continued until the signal from the fumigantconcentration sensor 22 indicates that the air flow through the duct 18contains the required concentration of the fumigant.

It will be clear to agricultural and chemical engineers that thefeed-back loops established by the arrangement illustrated in FIG. 1will be effective to control the settings of the valves 17 and 21 toensure that at all times when a fumigating gas is blown into the grainmass 11, the concentration of phosphine (or other fumigant) in the gasremains constant as the flow rate of the gas is varied in accordancewith the instantaneously calculated value of Q_(f).

The equipment illustrated in FIG. 1 also includes pressure sensors 19 inthe grain mass 11. The pressure sensors 19 (which are each model EMA 84manometers manufactured by TSE Co Pty Ltd of Melbourne, Australia, inthe installation at Wallendbeen) play no part in the fumigant controlmechanism. They are used for static pressure measurements whichindependently measure the validity of the formula used to determineQ_(f) , and the efficacy of the control mechanisms.

The full-scale testing of the present invention involves a series ofinvestigations, each having three phases. In the first phase of eachinvestigation, the gas flow through the grain mass 11 is controlled inaccordance with the derived formula for Q_(f), using the arrangementshown in FIG. 1, for a period of up to five days. Subsequently, in thesecond phase of the investigation, the flow of fumigating gas throughthe grain silo is established in accordance with the fumigationtechnique described and claimed in the specification of Australianpatent No 640,669 (which is the patent granted on the Australian patentapplication derived from International patent application NoPCT/AU90/00268). That is, a pre-determined flow of fumigant-containinggas, related to the cross-sectional area of the silo, is established.The second phase is also carried out for a period of up to five days. Inthe third phase of each investigation, the static pressurecharacteristics within the grain mass are monitored, using a number ofpressure sensors 19, in the absence of a gas flow through the duct 18.

Instead of the control arrangement illustrated in FIG. 1, themicroprocessor 13 could be programmed (a) to control air flow through ableed line 24 connected to the duct 18, or (b) to control the setting ofa speed control 27 for the blower 15. The second of these twoalternative control arrangements, both of which are shown with dashedlines in FIG. 1, is not preferred.

A typical set of data, obtained over one period of 24 hours during afirst phase of an observation at Wallendbeen, is shown in graphical formin FIG. 2. The three traces in FIG. 2 show

(i) the average temperature within the grain mass, as measured by thesensors 12 (the trace with values shown by solid squares);

(ii) the flow rate through the silo as calculated by the formula forQ_(f) of the present invention (the trace with values shown by solidtriangles); and

(iii) the actual flow through the silo (the trace with values shown bydots) of air containing a predetermined concentration of phosphine.

These data show clearly the ability of the controlling mechanisms toadjust the flow rate of the fumigant gas in the silo quickly andaccurately, and thus demonstrate the suitability of the presentinvention for use in the fumigation of stored foodstuffs in a top-ventedvertical silo in which a chimney effect flow can be expected.

The present invention can also be used in the continuous fumigation of anumber of similar silos in a grain storage facility, using a singlesource of fumigant gas, connected by respective ducts to the silos. Toensure that the charge of each silo is properly fumigated, temperaturesensors are installed in each silo, and the controller of thefumigant-containing gas uses the maximum value of the difference betweena grain temperature and the ambient air temperature outside the silos ofthe facility to determine the value of the rate of flow, Q_(f), offumigant-containing gas to the silos. With this arrangement, althoughone (or more) of the silos may receive the fumigant-containing gas at ahigher rate than that which is necessary to compensate for theindividual chimney effect (or chimney effects), none of the silos willexperience a dilution of the fumigant concentration in its associatedgrain mass.

If the ducts to the silos in the storage facility are not completelysymmetrical, then each silo will be provided with the arrangement oforifice plate and control valve that is described, for a multi-silofacility, in the specification of International patent application NoPCT/AU90/00268 (WIPO Publication No WO 91/00017).

Although exemplary implementations of the present invention have beendescribed above, it should be appreciated that variations in thoseimplementations may be effected without departing from the presentinventive concept. For example, the formulae given in the abovedescription for Q_(f) and Q_(c) are correct when the silo is full of thecommodity. If the silo is only partially filled with a commodity, thecalculated value of Q_(c) and Q_(f) needs to be multiplied by a factorh₅ /h_(g), where h_(s) is the height of the silo and h_(g) is the heightof the commodity in the silo.

We claim:
 1. A method of fumigation of a particulate commodity stored ina silo, said method comprising the steps of(a) providing a supply of afumigant-containing gas having a fumigant concentration which iseffective to control insect pests in the stored commodity when appliedto the stored commodity for an extended period; and (b) supplying thefumigant-containing gas to the base of the silo at a flow rate, Q_(f),which is determined, for a full silo, by the relationship ##EQU8## whereQ_(f) is expressed in m³ sec⁻¹ ; g is the acceleration due to gravity;P_(a) is the atmospheric pressure expressed in Pascals; R_(a) is the gasconstant for air; T_(a) is the temperature of the air outside the silo,expressed in K; T_(g) is the temperature of the commodity within thesilo, also in K; R is a resistance factor in Pascals sec m⁻² whichdepends upon the nature of the stored commodity in the silo; and A isthe horizontal cross-sectional area of the silo, in squaremeters;whereby the possible dilution of the fumigant concentrationwithin the commodity, as a result of the chimney effect, is prevented.2. A method of fumigation of a particulate commodity stored in a silo,said method comprising the steps of(a) providing a supply of afumigant-containing gas having a fumigant concentration which iseffective to control insect pests in the stored commodity when appliedto the stored commodity for an extended period; (b) ascertaining themaximum value of the difference between the temperature of the commoditywithin the silo and the ambient air temperature outside the silo whichwill be experienced for the period of fumigation of the commodity; (c)calculating the flow rate Q_(fmax), which is the value of Q_(f) which isobtained, using the formula ##EQU9## where Q_(f) is expressed in m³sec⁻¹ ; g is the acceleration due to gravity; P_(a) is the atmosphericpressure expressed in Pascals; R_(a) is the gas content for air; T_(a)is the temperature of the air outside the silo, expressed in K; T_(g) isthe temperature of the commodity within the silo, also in K; R is aresistance factor in Pascals sec m⁻² which depends upon the nature ofthe stored commodity in the silo; and A is the horizontalcross-sectional area of the silo, ikn square meters; when said maximumtemperature difference is used to determine Q_(f) ; and (d) supplyingsaid fumigant-containing gas to the base of the silo at a constant rateof Q_(fmax) ;whereby said method of fumigation may be performedunattended without a possible reduction of the fumigant concentration insaid commodity, due to the chimney effect, to a value below the minimumfumigant concentration that is required for effective fumigation of saidcommodity.
 3. A fumigation method as defined in claim 1, in which thesupply of fumigant-containing gas to the base of the silo is effectedcontinuously by a control mechanism which includes a programmedmicroprocessor or a programmed computer that is responsive to signalscorresponding to the instantaneous values of T_(a) and T_(g).
 4. Afumigation method as defined in claim 1 in which there is apredetermined minimum value of said flow rate, which is maintained whenthe calculated value of Q_(f) is less than said minimum flow rate value.5. A method of fumigation of a plurality of silos in a storage facility,each silo in said facility containing a respective particulatecommodity, said method comprising the steps of(a) providing a supply ofa fumigant-containing gas having a fumigant concentration which iseffective to control insect pests in the stored commodity orcommodities; and (b) monitoring the temperature, T_(g), of the commodityin each silo and also the ambient air temperature, T_(a), outside thesilos, and determining the maximum value of the difference between thetemperature of a stored commodity and said ambient air temperature; and(c) supplying the fumigant-containing gas to the bases of the silos at aflow rate, Q_(f), which is determined by the relationship ##EQU10##where Q_(f) is expressed in m³ sec⁻¹ ; g is the acceleration due togravity P_(a) is the atmospheric pressure expressed in Pascals; R_(a) isthe gas constant for air; T_(a) is the temperature of the air outsidethe silos, expressed in K; T_(g) is the temperature of a commodity in asilo which differs most from T_(a), also in K; R is a resistance factorin Pascals sec m⁻² which depends upon the nature of the storedcommodities in the silos; and A is the sum of the horizontalcross-sectional areas of the silos, in square meters;whereby thepossible dilution of the fumigant concentration in any silo in thefacility to a value below that required for effective fumigation of thestored commodity, due to the chimney effect, is prevented.
 6. Afumigation method as defined in claim 1 in which the commodity is grain.7. A fumigation method as defined in claim 1, in which the fumigant inthe fumigant-containing gas is phosphine.
 8. Apparatus for fumigating aparticulate commodity which is stored in a silo, said apparatuscomprising:(a) means for pumping a fumigant-containing gas into the baseof the silo; (b) first temperature sensing means positioned within thecommodity in the silo and having a first output signal indicative of thetemperature within the stored commodity; (c) second temperature sensingmeans positioned outside the silo and having a second output signalindicative of the ambient air temperature outside the silo; (d)processing means adapted to receive said first and second output signalsand generate at least one control signal; said at least one controlsignal being input to control means; said control means being adapted tocontrol the rate at which the fumigant-containing gas is pumped by saidpumping means so that the rate of flow of the fumigant-containing gasinto the silo has a value, Q_(f), which is determined, for a full silo,by the relationship ##EQU11## where Q_(f) is expressed in m³ sec⁻¹ ; gis the acceleration due to gravity; P_(a) is the atmospheric pressureexpressed in Pascals; R_(a) is the gas constant for air; T_(a) is thetemperature of the air outside the silo, expressed in K; T_(g) is thetemperature of the commodity within the silo, also in K; R is aresistance factor in Pascals sec m⁻¹ which depends upon the nature ofthe commodity in the silo; and A is the horizontal cross-sectional areaof the silo, in m².
 9. Fumigation apparatus as defined in claim 8, inwhich(a) said control means comprises (i) a first valve in a ductextending from an air blower to the base of the silo and (ii) a secondvalve in a line extending from a pressurised source of fumigant gas tosaid duct; (b) said control means controls said first valve to establisha flow rate of air into said silo in accordance with the calculatedvalue of Q_(f) ; and (c) said control means controls said second valveto maintain a predetermined concentration of fumigant in the air flowingthrough said duct.
 10. Apparatus for fumigating a plurality of silos ina storage facility, each of said silos containing a particulatecommodity, said apparatus comprising:(a) means for pumping afumigant-containing gas from a single source into the base of each silo;(b) a respective first temperature sensing means positioned within thecommodity in each silo, each of said first temperature sensing meanshaving a respective first output signal indicative of the temperature,T_(g), of its associated commodity; (c) second temperature sensing meanspositioned outside the silos and having a second output signalindicative of the ambient air temperature, T_(a), outside the silo; (d)processing means operatively connected to said temperature sensing meansand to control means, said processing means being adapted to receivesaid first output signals and said second output signal and determinethe maximum difference between the temperature of a commodity and theambient air temperature, and to generate a control signal, said controlsignal being input to said control means; said control means beingadapted to control the rate at which said gas pumping means pumps thefumigant-containing gas into the silos so that the rate of flow of thefumigant-containing gas into the silos has a value, Q_(f), which iscalculated using the formula ##EQU12## where Q_(f) is expressed in m³sec⁻¹ ; g is the acceleration due to gravity; P_(a) is the atmosphericpressure expressed in Pascals; R_(a) is the gas constant for air; T_(a)is the temperature of the air outside the silos, expressed in K; T_(g)is the temperature of a commodity in a silo which differs most fromT_(a), also in K; R is a resistance factor in Pascals sec m⁻² whichdepends upon the nature of the stored commodities in the silos; and A isthe sum of the horizontal cross-sectional areas of the silos, in squaremeters.
 11. Fumigation apparatus as defined in claim 8, in which saidprocessing means is a programmed microprocessor or a programmedcomputer.
 12. Fumigation apparatus as defined in claim 8, includingmeans to maintain a predetermined minimum value of said flow rate whenthe calculated value of Q_(f) is less than said minimum flow rate value.13. A fumigation method as defined in claim 1, in which the silo is onlypartially filled with a commodity, and the calculated value of Q_(f) ismultiplied by a factor f, wheref=h_(s) /h_(g), h_(s) is the height ofthe silo, and h_(g) is the height of the commodity in the silo. 14.Fumigation apparatus as defined in claim 8, in which the silo is onlypartially filled with a commodity, and the calculated value of Q_(f) ismultiplied by a factor f, wheref=h_(s) /h_(g), h_(s) is the height ofthe silo, and h_(g) is the height of the commodity in the silo.
 15. Afumigation method as defined in claim 5, in which each silo is onlypartially filled with a commodity, and the calculated value of Q_(f) ismultiplied by a factor f, wheref=h_(s) /h_(g), h_(s) is the height ofthe silo, and h_(g) is the height of the commodity in the silo. 16.Fumigation apparatus as defined in claim 10, including means to maintaina predetermined minimum value of said flow rate when the calculatedvalue of Q_(f) is less than said minimum flow rate value.
 17. Fumigationapparatus as defined in claim 10, in which each silo is only partiallyfilled with a commodity, and the calculated value of Q_(f) is multipliedby a factor f, wheref=h_(s) /h_(g), h_(s) is the height of the silo, andh_(g) is the height of the commodity in the silo.
 18. A fumigationmethod as defined in claim 1, in which the commodity is selected fromthe group consisting of commodities listed in the table below, and R isthe value of R calculated for said commodity and is also listed in thetable below:

    ______________________________________                                        Commodity                R                                                    ______________________________________                                        Alfalfa                  16,318                                               Barley                   1,676                                                Clover, alsike           27,263                                               Clover, crimson          10,455                                               Clover, red              17,626                                               *Corn, clean ear         6.19                                                 *Corn, ear, as harvested 128                                                  Corn, shelled            719                                                  Fescue                   4,722                                                Flax                     10,421                                               Grass seed, brome        1,535                                                Grass seed, rescue       709                                                  Kobe Lespedeza           3,167                                                Lupin seed, blue         512                                                  Oats                     1.816                                                *Pea beans               435                                                  *Peanuts in shell        29.0                                                 Popcorn, shelled, yellow pearl                                                                         1,046                                                type                                                                          Popcorn, white rice type 1,766                                                Rice, rough              1,952                                                Sericea Lespedeza        16,318                                               Sorghum, grain           2,664                                                Soybeans                 646                                                  Wheat                    3,131                                                Linseed, glenelg         14,907                                               Rapeseed, tower          7,097                                                Safflower, gila          1,207                                                Sunflower, commercial crushing                                                                         1,593                                                ______________________________________                                         *Approximate value                                                       